ANALISI DELLE ISTITUZIONI POLITICHE corso progredito

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Positive political Theory an introduction General
information
Credits 6 (40 hours) for both EPS curricula
(EPAPPP) 3 (20 hours) for Ph.D Students in
Political Studies (Political Science)? Period
21st September - 30th November Instructor
Francesco Zucchini (francesco.zucchini_at_unimi.it
) Office hours Monday 17-19, room 308, third
floor, Dpt. Studi Sociali e Politici
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Course aims, structure, assessment

• The course is an introduction to the study of
  politics from a rational choice perspective.
• Students are introduced both to the analytical
  tools of the approach and to the results most
  relevant to the political science. We will focus
  on the institutional effects of decision-making
  processes and on the nature of political actors
  in the democracies.
• All students are expected to do all the reading
  for each class session and may be called upon at
  any time to provide summary statements of it.
• Evaluation of all students is based upon the
  regular participation in the classroom
  activities (30) and a final written exam.
• Evaluation of Ph.Students is also based upon
  individual presentations (30).

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Positive political Theory An introduction
Lecture 1 Epistemological foundation of the
Rational Choice approach Francesco Zucchini
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What the rational choice is not
NON RATIONAL CHOICE THEORIES

• Theories with non rational actors
• Relative deprivation theory
• Imitation instinct (Tarde)
• False consciouness (Engels)
• Inconscient pulsions (Freud)
• Habitus (Bourdieu)

• Theories without actors
• System analysis
• Structuralism
• Functionalism (Parsons)

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What the rational choice is

• Weak Requirements of Rationality
• 1) Impossibility of contradictory beliefs or
  preferences
• 2) Impossibility of intransitive preferences
• 3) Conformity to the axioms of probability
  calculus

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Weak requirements of Rationality

• 1) Impossibility of contradictory beliefs or
  preferences
• if an actor holds contradictory beliefs she
  cannot reason
• if an actor hold contradictory preferences she
  can choose any option
• Important contradiction refers to beliefs or
  preferences at a given moment in time.

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Weak requirements of Rationality

• 2) Impossibility of intransitive preferences
• if an actor prefers alternative a over b and b
  over c , she must prefer a over c .
• One can create a money pump from a person with
  intransitive preferences.
• Person Z has the following preference ordering
• agtbgtcgta she holds a. I can persuade her to
  exchange a for c provided she pays 1 then I can
  persuade her to exchange c for b for 1 more
  again I can persuade her to pay 1 to exchange b
  for a. She holds a as at the beginning but she is
  3 poorer

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Weak requirements of Rationality

• 3) Conformity to the axioms of probability
  calculus
• A1 No probability is less than zero. P(i)gt0
• A2 Probability of a sure event is one
• A3 If i and j are two mutually exclusive events,
  then P (i or j) P(i )P(j)?

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A small quantity of formalization...

• A choice between different alternatives
• S (s1, s2, si)?
• Each alternative can be put on a nominal, ordinal
  o cardinal scale
• The choice produces a result
• R (r1, r2, ri)?
• An actor chooses as a function of a preference
  ordering relation among the results. Such
  ordering is
• complete
• transitive

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Utility

• A ( mostly) continuous preference ordering
  assigns a position to each result
• We can assign a number to such ordering called
  utility
• A result r can be characterized by these features
  (x,y,z) to which an utility value u f(x,y,z)
  corresponds
• Rational action maximizes the utility function

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Single-peak utility functions

• One dimension (the real line)?
• Actor with ideal point A, outcome x
• Linear utility function
• U - x A
• Quadratic utility function
• U - (x A)2

-

-
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Expected utility

• There could be unknown factors that could come in
  between a choice of action and a result
• .. as a function of different states of the world
  M (m1, m2, mi)?
• Choice under uncertainty is based associating
  subjective probabilities to each state of the
  world, choosing a lottery of results L
  (r1,p1r2,p2 ri,pi)?
• We have then an expected utility function
• EU u(r1)p1u(r2)p2 u(ri)pi

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Strong Requirements of Rationality

• 1) Conformity to the prescriptions of game theory
• 2) Probabilities approximate objective
  frequencies in equilibrium
• 3) Beliefs approximate reality in equilibrium

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Strong Requirements of Rationality

• 1) Conformity to the prescriptions of game
  theory digression..
• Uncertainty between choices and outcomes could
  also result from the (unknown) decisions taken by
  other rational actors
• Game theory studies the strategic interdependence
  between actors, how one actors utility is also
  function of other actors decisions, how actors
  choose best strategies, and the resulting
  equilibrium outcomes

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Principles of game theory

• Players have preferences and utility functions
• Game is represented by a sequence of moves
  (actors or Nature choices)?
• How information is distributed is key
• Strategy is a complete action plan, based on the
  anticipation of other actors decisions
• A combination of strategies determines an outcome
• This outcome determines a payoff to each player,
  and a level of utility (the payoff is an argument
  of the players utility function)?

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Principles of game theory (2)?

• Games in the extensive form are represented by a
  decision tree
• which illustrates the possible conditional
  strategic options
• The distribution of information
  complete/incomplete (game structure),
  perfect/imperfect (actors types), common
  knowledge

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Principles of game theory (3)?

• Solutions is by backward induction, by
  identifying the subgame perfect equilibria
• Nash equilibrium the profile of the best
  responses, conditional on the anticipation of
  other actors best responses
• A Nash equilibrium is stable no-one unilaterally
  changes strategy

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Strong Requirements of Rationality

• 2) Subjective probabilities approximate objective
  frequencies in equilibrium.
• Every player makes the best use of his
  previous probability assessments and the new
  information that he gets from the environment.
• Beliefs are updated according to Bayess rule.

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Strong Requirements of Rationality
Bayesian updating of beliefs
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Strong Requirements of Rationality

• 3) Beliefs should approximate reality
• Beliefs and behavior not only have to be
  consistent but also have to correspond with the
  real world at equilibrium

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Rational Choice only a normative theory ?

• Usual criticism to the Rational Choice theory
• In the real world people are incapable of making
  all the required calculations and computations.
  Rational choice is not realistic
• Usual answer (M.Friedman) people behave as if
  they were rational
• In so far as a theory can be said to have
  assumptions at all, and in so far as their
  realism can be judged independently of the
  validity of predictions, the relation between the
  significance of a theory and the realism of its
  assumptions is almost the opposite of that
  suggested by the view under criticism. Truly
  important and significant hypotheses will be
  found to have assumptions that are wildly
  inaccurate descriptive representations of
  reality, and, in general, the more significant
  the theory, the more unrealistic the assumptions
  (in this sense). The reason is simple. A
  hypothesis is important if it explains much by
  little, that is, if it abstracts the common and
  crucial elements from the mass of complex and
  detailed circumstances surrounding the phenomena
  to be explained and permits valid predictions on
  the basis of them alone. To be important,
  therefore, a hypothesis must be descriptively
  false in its assumptions it takes account of,
  and accounts for, none of the many other
  attendant circumstances, since its very success
  shows them to be irrelevant for the phenomena to
  be explained.
• As if argument claims that the rationality
  assumption, regardless of its accuracy, is a way
  to model human behaviour
  Rationality as model argument (look at Fiorina
  article)

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Rational Choice only a normative theory ?

• Tsebelis counter argument to rationality as
  model argument
• 1)the assumptions of a theory are, in a trivial
  sense, also conclusions of the theory . A
  scientist who is willing to make the wildly
  inaccurate assumptions Friedman wants him to
  make admits that wildly inaccurate behaviour
  can be generated as a conclusion of his theory.
• 2) Rationality refers to a subset of human
  behavior. Rational choice cannot explain every
  phenomenon. Rational choice is a better approach
  to situations in which the actors identity and
  goals are established and the rules of
  interaction are precise and known to the
  interacting agents.
• Political games structure the situation as well
  the study of political actors under the
  assumption of rationality is a legitimate
  approximation of realistic situations, motives,
  calculations and behavior.
• 5 arguments

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Five arguments in defense of the Rational Choice
Approach (Tsebelis)

• Salience of issues and information
• Learning
• Heterogeneity of individuals
• Natural Selection
• Statistics

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Five arguments in defense of the Rational Choice
Approach (Tsebelis)

• 3) Heterogeneity of individuals equilibria with
  some sophisticated agents (read fully rational)
  will tend toward equilibria where all agents are
  sophisticated in the cases of congestion
  effects , that is where each agent is worse off
  the higher the number of other agents who make
  the same choice as he. An equilibrium with a
  small number of sophisticated agents is
  practically indistinguishable from an equilibrium
  where all agents are sophisticated

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Five arguments in defense of the Rational Choice
Approach (Tsebelis)

• 3) Statistics rationality is a small but
  systematic component of any individual , and all
  other influences are distributed at random. The
  systematic component has a magnitude x and the
  random element is normally distributed with
  variance s. Each individual of population will
  execute a decision in the interval x-(2s),
  x(2s) 95 percent of the time. However in a
  sample of a million individuals the average
  individual will make a decision in the interval
  x-(2s/1000), x(2s/1000) 95 percent of the time

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Rational choice a theory for the institutions

• In the rational choice approach individual
  action is assumed to be an optimal adaptation to
  an institutional environment, and the interaction
  among individuals is assumed to be an optimal
  response to each other. The prevailing
  institutions (the rules of the game) determine
  the behavior of the actors, which in turn
  produces political or social outcomes.
• Rational choice is unconcerned with individuals
  or actors per se and focuses its attention on
  political and social institutions

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Advantages of the Rational choice Approach

• Theoretical clarity and parsimony
• Ad hoc explanations are eliminated
• Equilibrium analysis
• Optimal behavior is discovered, it is easy to
  formulate hypothesis and to eliminate alternative
  explanations.
• Deductive reasoning
• In RC we deal with tautology. If a model does not
  work , as the model is still correct, you have to
  change the assumption (usually the structure of
  the game..).Therefore also the wrong models are
  useful for the cumulation of the knowledge.
• Interchangeability of individuals

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Positive political Theory An introduction
Lecture 2 Basic tools of analytical politics
Francesco Zucchini
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Spatial representation

• In case of more than one dimension, we have
  iso-utility curves (indifference curves)
• Utility diminishes as we move away from the ideal
  point
• The shape of the iso-utility curve varies as a
  function of the salience of the dimensions

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Continuous utility functions in 1 dimension
Spatial representation
Utility
Dimension x
xi
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..and in 2 Dimensions
Iso-utility curves or indifference curves
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Spatial representation

• In case of more than one dimension, we have
  iso-utility curves (indifference curves)
• Utility diminishes as we move away from the ideal
  point
• The shape of the iso-utility curve varies as a
  function of the salience of the dimensions

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Indifference curve
Player I prefers a point which is inside the
indifference curve (such as P) to one outside
(such as Z), and is indifferent between two
points on the same curve (like X and Y)?
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A basic equation in positive political theory

• Preferences x Institutions Outcomes
• Comparative statics (i.e. propositions) that form
  the basis to testable hypotheses can be derived
  as follows
• As preferences change, outcomes change
• As institutions change, outcomes change

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A typical institution a voting rule

• Committee/assembly of N members
• K p N minimum number of members to approve a
  committees decision
• In Simple Majority Rule (SMR) K gt (1/2)N
• Of course, there are several exceptions to SMR
• Filibuster in the U.S. Senate debate must end
  with a motion of cloture approved by 3/5 (60 over
  100) of senators
• UE Council of Ministers qualified majority (255
  votes out of 345, 73.9 )
• Bicameralism

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A proposition the voting paradox

• If a majority prefers some alternatives to x,
  these set of alternatives is called winset of x,
  W(x) if an alternative x has an empty winset ,
  W(x)Ø, then x is an equilibrium, namely is a
  majority position that cannot be defeated.
• If no alternative has an empty winset then we
  have cycling majorities
• SMR cannot guarantee a majority position a
  Condorcet winner which can beat any other
  alternative in pairwise comparisons. In other
  terms SMR cannot guarantee that there is an
  alternative x whose W(x)Ø

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Condorcet Paradox

• Imagine 3 legislators with the following
  preferences orders
• Alternatives can be chosen by majority rule
• Whoever control the agenda can completely control
  the outcome

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1,2 choose z against x but..
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2,3 choose y against z but again..
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1,3 choose x against y.. z defeats x that defeats
y that defeats z.
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Whoever control the agenda can completely control
the outcome

• Imagine a legislative voting in two steps. If Leg
  1 is the agenda setter..

y
x
x
z
z
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Whoever control the agenda can completely control
the outcome

• If Leg 2 is the agenda setter..

x
z
z
y
y
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Whoever control the agenda can completely control
the outcome

• If Leg 3 is the agenda setter.

y
z
y
x
x
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Probability of Cyclical Majority
Number of Voters (n) Number of Voters (n) Number of Voters (n) Number of Voters (n) Number of Voters (n) Number of Voters (n)
N.Alternatives (m) 3 5 7 9 11 limit
3 0.056 0.069 0.075 0.078 0.080 0.088
4 0.111 0.139 0.150 0.156 0.160 0.176
5 0.160 0.200 0.215 0.251
6 0.202 0.315
Limit ?1.000 ?1.000 ?1.000 ?1.000 ?1.000 ?1.000

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Median voter theorem

• A committee chooses by SMR among alternatives
• Single-peak Euclidean utility functions
• Winset of x W(x) set of alternatives that beat x
  in a committee that decides by SMR
• Median voter theorem (Black) If the member of a
  committee G have single-peaked utility functions
  on a single dimension, the winset of the ideal
  point of the median voter is empty. W(xmed)Ø

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When the alternatives can be disposed on only one
dimension namely when the utility curves of each
member are single peaked then there is a
Condorcet winner the median voter
Utility
1
2
3
y
z
x
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When the alternatives can be disposed on only one
dimension namely when the utility curves of each
member are single peaked then there is a
Condorcet winner the median voter
Utility
1
2
3
x
y
z
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When there is a Condorcet paradox (no winner)
then the alternatives cannot be disposed on only
one dimension namely the utility curves of each
member are not single peaked
2 peaks
Utility
1
2
3
x
z
y
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When there is a Condorcet paradox (no winner)
then the alternatives cannot be disposed on only
one dimension namely the utility curves of each
legislator are not ever single peaked
2 peaks
Utility
1
2
3
y
z
x
In 2 or more dimensions a unique equilibrium is
not guaranteed
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Electoral competition and median voter theorem
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Theorems

• Chaos Theorem (McKelvey) In a multi-dimensional
  space, there are no points with a empty winset or
  no Condocet winners, if we apply SMR (with one
  exception, see below). There will be chaos and
  the agenda setter (i.e. which controls the order
  of voting) can determine the final outcome
• Plot Theorem In a multi-dimensional space, if
  actors ideal points are distributed radially and
  symmetrically with respect to x, then the winset
  of x is empty
• Change of rules, institutions (bicameralism,
  dimension-by-dimension voting) can produce a
  stable equilibrium

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Cycling majorities
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Plotts Theorem
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Plotts Theorem
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Instability, majority rule and multidimensional
space
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How institutions can affect the stability (and
the nature) of the decisions ? Example with
bicameralism
Imagine 6 legislators in one chamber and the
following profiles of preferences.
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2,3,5,6 prefer x to z but..
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1,4,5,6 prefer w to x, but..
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all prefer y to w, but..
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1,2,3,4 prefer z to y, .CYCLE!
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Imagine that the same legislators are grouped in
two chambers in the following way (red chamber
1,2,3 and blue chamber 4,5,6) and that the final
alternative must win a majority in both chambers.
2, 3, and 5, 6 prefer x to z
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However now w cannot be preferred to x as in the
Red Chamber only 1 prefers w to x. once approved
against z , x cannot be defeated any longer What
happen if we start the process with y ? All
legislators prefer y to w..
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• However now z cannot be chosen against y as in
  the Blue Chamber only 4 prefers z to y. once
  approved against w , y cannot be defeated any
  longer.
• We have two stable equilibria x and y. The final
  outcome will depend on the initial status quo
  (SQ)?
• If x (y) is the SQ then the final outcome will
  be x (y)?
• If z (w) is the SQ then the final outcome will be
  x (y)?